Average Error: 15.2 → 0.8
Time: 17.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r22932134 = g;
        double r22932135 = 2.0;
        double r22932136 = a;
        double r22932137 = r22932135 * r22932136;
        double r22932138 = r22932134 / r22932137;
        double r22932139 = cbrt(r22932138);
        return r22932139;
}
↓
double f(double g, double a) {
        double r22932140 = g;
        double r22932141 = cbrt(r22932140);
        double r22932142 = 2.0;
        double r22932143 = a;
        double r22932144 = r22932142 * r22932143;
        double r22932145 = cbrt(r22932144);
        double r22932146 = r22932141 / r22932145;
        return r22932146;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]

  4. Taylor expanded around 0 33.8

    \[\leadsto \frac{\color{blue}{{g}^{\frac{1}{3}}}}{\sqrt[3]{2 \cdot a}}\]

  5. Simplified0.8

    \[\leadsto \frac{\color{blue}{\sqrt[3]{g}}}{\sqrt[3]{2 \cdot a}}\]

  6. Final simplification0.8

    \[\leadsto \frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))